The "slot-drill" completion method, which utilizes a mechanically cut high-conductivity "slot" in the target formation created using a tensioned abrasive cable, has been proposed as an alternative stimulation technique for shale-gas and other low/ultra-low permeability formations. This thesis provides a comprehensive numerical simulation study on the "slot drill" completion technique. Using a Voronoi gridding scheme, I created representative grid systems for the slot-drill completion, as well as for the case of a vertical well with a single fracture, the case of a horizontal well with multiple hydraulic fractures, and various combinations of these completions. I also created a rectangular slot configuration, which is a simplified approximation of the actual "slot-drill" geometry, and investigated the ability of this rectangular approximation to model flow from the more complicated (actual) slot-drill configuration(s). To obtain the maximum possible diagnostic and analytical value, I simulated up to 3,000 years of production, allowing the assessment of production up to the point of depletion (or boundary-dominated flow). These scenarios provided insights into all the various flow regimes, as well as provided a quantitative evaluation of all completion schemes considered in the study. The results of my study illustrated that the "slot-drill" completion technique was not, in general, competitive in terms of reservoir performance and recovery compared to the more traditional completion techniques presently in use. Based on my modeling, it appears that the larger surface area to flow that multistage hydraulic fracturing provides is much more significant than the higher conductivity achieved using the slot-drill technique. This work provides quantitative results and diagnostic interpretations of productivity and flow behavior for low and ultra-low permeability formations completed using the slot-drill method. The results of this study can be used to (a) help evaluate the possible application of the "slot-drill" technique from the perspective of performance and recovery, and (b) to establish aggregated economic factors for comparing the slot-drill technique to more conventional completion and stimulation techniques applied to low and ultra-low permeability reservoirs.